Hey there,

A new user just asked for the back story behind Daily Coding Problem, so I thought I would share it with you as well.

A while back, my friends were practicing for coding interviews, and I started a group chat where we tried to solve a coding problem every day.

It worked insanely well — all of them got offers from top tech companies and startups.

Fast forward, I started Daily Coding Problem with a buddy. The original website was ridiculously hideous:

Daily Coding Problem is like that group chat, trying to solve a coding interview question together. What I love is that with consistent practice, you get much faster and better at coming up with solutions.

We've found that working on the same problems with your friends helps a lot with motivation. Just send them this link — https://www.dailycodingproblem.com — and tell them to subscribe. With daily practice, I’m sure you’ll land that dream job offer. Good luck and happy studying!

Marc

Founder

Good morning! Here's your coding interview problem for today.

This problem was recently asked by Google.

Given a list of numbers and a number k, return whether any two numbers from the list add up to k.

For example, given [10, 15, 3, 7] and k of 17, return true since 10 + 7 is 17.

Bonus: Can you do this in one pass?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Uber.

Given an array of integers, return a new array such that each element at index i of the new array is the product of all the numbers in the original array except the one at i.

For example, if our input was [1, 2, 3, 4, 5], the expected output would be [120, 60, 40, 30, 24]. If our input was [3, 2, 1], the expected output would be [2, 3, 6].

Follow-up: what if you can't use division?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given the root to a binary tree, implement serialize(root), which serializes the tree into a string, and deserialize(s), which deserializes the string back into the tree.

For example, given the following Node class

class Node:

    def __init__(self, val, left=None, right=None):

        self.val = val

        self.left = left

        self.right = right

The following test should pass:

node = Node('root', Node('left', Node('left.left')), Node('right'))

assert deserialize(serialize(node)).left.left.val == 'left.left'

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Good morning! Here's your coding interview problem for today.

This problem was asked by Stripe.

Given an array of integers, find the first missing positive integer in linear time and constant space. In other words, find the lowest positive integer that does not exist in the array. The array can contain duplicates and negative numbers as well.

For example, the input [3, 4, -1, 1] should give 2. The input [1, 2, 0] should give 3.

You can modify the input array in-place.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Jane Street.

cons(a, b) constructs a pair, and car(pair) and cdr(pair) returns the first and last element of that pair. For example, car(cons(3, 4)) returns 3, and cdr(cons(3, 4)) returns 4.

Given this implementation of cons:

def cons(a, b):

    def pair(f):

        return f(a, b)

    return pair

Implement car and cdr.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

An XOR linked list is a more memory efficient doubly linked list. Instead of each node holding next and prev fields, it holds a field named both, which is an XOR of the next node and the previous node. Implement an XOR linked list; it has an add(element) which adds the element to the end, and a get(index) which returns the node at index.

If using a language that has no pointers (such as Python), you can assume you have access to get_pointer and dereference_pointer functions that converts between nodes and memory addresses.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given the mapping a = 1, b = 2, ... z = 26, and an encoded message, count the number of ways it can be decoded.

For example, the message '111' would give 3, since it could be decoded as 'aaa', 'ka', and 'ak'.

You can assume that the messages are decodable. For example, '001' is not allowed.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

A unival tree (which stands for "universal value") is a tree where all nodes under it have the same value.

Given the root to a binary tree, count the number of unival subtrees.

For example, the following tree has 5 unival subtrees:

   0

  / \

 1   0

    / \

   1   0

  / \

 1   1

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Good morning! Here's your coding interview problem for today.

This problem was asked by Airbnb.

Given a list of integers, write a function that returns the largest sum of non-adjacent numbers. Numbers can be 0 or negative.

For example, [2, 4, 6, 2, 5] should return 13, since we pick 2, 6, and 5. [5, 1, 1, 5] should return 10, since we pick 5 and 5.

Follow-up: Can you do this in O(N) time and constant space?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Apple.

Implement a job scheduler which takes in a function f and an integer n, and calls f after n milliseconds.

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Hey there,

Hope your day is going well! I wrote a tutorial on how to solve hard interview questions and thought you might be interested.

So let's go over the thought process for solving tricky coding interview questions. I often find it's not enough to just be able to solve the problem; you really need to vocalize your thought process. This shows that you're a strong communicator and that you didn't just get lucky solving this one particular problem.

The question we'll work through is the following: return a new sorted merged list from K sorted lists, each with size N. Before we move on any further, you should take some time to think about the solution!

1. First, go through an example. This buys time, makes sure you understand the problem, and lets you gain some intuition for the problem. For example, if we had [[10, 15, 30], [12, 15, 20], [17, 20, 32]], the result should be [10, 12, 15, 15, 17, 20, 20, 30, 32].

2. Next, give any solution you can think of (even if it's brute force). It seems obvious that if we just flattened the lists and sorted it, we would get the answer we want. The time complexity for that would be O(KN log KN), since we have K * N total elements.

3. The third step is to think of pseudocode—a high-level solution for the problem. This is where we explore different solutions. The things we are looking for are better space/time complexities but also the difficulty of the implementation. You should be able to finish the solution in 30 minutes. Here, we can see that we only need to look at K elements in each of the lists to find the smallest element initially. Heaps are great for finding the smallest element. Let's say the smallest element is E. Once we get E, we know we're interested in only the next element of the list that held E. Then we'd extract out the second smallest element and etc. The time complexity for this would be O(KN log K), since we remove and append to the heap K * N times.

4. Initialize the heap. In Python this this is just a list. We need K tuples. One for the index for which list among the list of lists the element lives; one for the element index which is where the element lives; and the value of the element. Since we want the key of the heap to be based on the value of the element, we should put that first in the tuple.

5. While the heap is not empty we need to:
   • Extract the minimum element from the heap: (value, list index, element index)
   • If the element index is not at the last index, add the next tuple in the list index.

4. Write the actual code. Ideally, at this point, it should be clear how the code should look like. Here's one example:

def merge(lists):

    merged_list = []



    heap = [(lst[0], i, 0) for i, lst in enumerate(lists) if lst]

    heapq.heapify(heap)



    while heap:

        val, list_ind, element_ind = heapq.heappop(heap)



        merged_list.append(val)



        if element_ind + 1 < len(lists[list_ind]):

            next_tuple = (lists[list_ind][element_ind + 1],

                          list_ind,

                          element_ind + 1)

            heapq.heappush(heap, next_tuple)

    return merged_list

5. Think of test cases and run them through your interviewer. This shows that you're willing to test your code and ensure it's robust. I like to think of happy cases and edge cases. Our original example would be a happy case. Edge cases might be.

   • lists is [].
   • lists only contains empty lists: [[], [], []].
   • lists contains empty lists and non-empty lists: [[], [1], [1,2]].
   • lists contains one list with one element: [[1]].
   • lists contains lists of varying size: [[1], [1, 3, 5], [1, 10, 20, 30, 40]].

6. Finally, the interviewer should ask some follow-up questions. One common question is: what other solutions are there? There's actually another relatively simple solution that would use a divide-and-conquer strategy. We could recursively merge each half of the lists and then combine the two lists. This would have the same asymptotic complexities but would require more "real" memory and time.

Doing all these steps will definitely help you crystallize your thought process, grasp the problem better, and show that you are a strong communicator and help you land that job offer!

Best of luck!

Marc

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Good morning! Here's your coding interview problem for today.

This problem was asked by Twitter.

Implement an autocomplete system. That is, given a query string s and a set of all possible query strings, return all strings in the set that have s as a prefix.

For example, given the query string de and the set of strings [dog, deer, deal], return [deer, deal].

Hint: Try preprocessing the dictionary into a more efficient data structure to speed up queries.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

There exists a staircase with N steps, and you can climb up either 1 or 2 steps at a time. Given N, write a function that returns the number of unique ways you can climb the staircase. The order of the steps matters.

For example, if N is 4, then there are 5 unique ways:

• 1, 1, 1, 1
• 2, 1, 1
• 1, 2, 1
• 1, 1, 2
• 2, 2

What if, instead of being able to climb 1 or 2 steps at a time, you could climb any number from a set of positive integers X? For example, if X = {1, 3, 5}, you could climb 1, 3, or 5 steps at a time.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given an integer k and a string s, find the length of the longest substring that contains at most k distinct characters.

For example, given s = "abcba" and k = 2, the longest substring with k distinct characters is "bcb".

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

The area of a circle is defined as πr^2. Estimate π to 3 decimal places using a Monte Carlo method.

Hint: The basic equation of a circle is x² + y² = r².

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a stream of elements too large to store in memory, pick a random element from the stream with uniform probability.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Twitter.

You run an e-commerce website and want to record the last N order ids in a log. Implement a data structure to accomplish this, with the following API:

• record(order_id): adds the order_id to the log
• get_last(i): gets the ith last element from the log. i is guaranteed to be smaller than or equal to N.

You should be as efficient with time and space as possible.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Suppose we represent our file system by a string in the following manner:

The string "dir\n\tsubdir1\n\tsubdir2\n\t\tfile.ext" represents:

dir

    subdir1

    subdir2

        file.ext

The directory dir contains an empty sub-directory subdir1 and a sub-directory subdir2 containing a file file.ext.

The string "dir\n\tsubdir1\n\t\tfile1.ext\n\t\tsubsubdir1\n\tsubdir2\n\t\tsubsubdir2\n\t\t\tfile2.ext" represents:

dir

    subdir1

        file1.ext

        subsubdir1

    subdir2

        subsubdir2

            file2.ext

The directory dir contains two sub-directories subdir1 and subdir2. subdir1 contains a file file1.ext and an empty second-level sub-directory subsubdir1. subdir2 contains a second-level sub-directory subsubdir2 containing a file file2.ext.

We are interested in finding the longest (number of characters) absolute path to a file within our file system. For example, in the second example above, the longest absolute path is "dir/subdir2/subsubdir2/file2.ext", and its length is 32 (not including the double quotes).

Given a string representing the file system in the above format, return the length of the longest absolute path to a file in the abstracted file system. If there is no file in the system, return 0.

Note:

The name of a file contains at least a period and an extension.

The name of a directory or sub-directory will not contain a period.

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Hey there,

Today I'd like to give you some tips on how to solve tree-based interview questions. Tree questions are very common at top tech company interviews. I had two tree questions in my Google onsite interviews and one during my Facebook onsite interviews. An awesome thing about them is that they can be formulaically solved every single time. It doesn’t involve any genius insight. Let me show you how.

Instead of being too abstract, let’s just dive right into an easy binary tree question. Then I’ll walk through how to solve it and we can go into a harder problem after:

Given the root to a binary tree, count the total number of nodes there are.

Before we move on further, feel free to take a moment to think about the answer!

Solving any binary tree question involves just two steps.

First is solving the base case. This usually means solving the leaf node case (a leaf node has no left or right children) or the null case. For the above problem, we can see that a null should represent 0 nodes while a leaf node should represent 1 node.

Second is the recursive step. Assuming you knew the solution to the left subtree and the right subtree, how could you combine the two results to give you the final solution? It’s important to not get caught up on how this works and just have faith that it works. If you start tracing the recursion, you’re going to needlessly use up time and energy during the interview. Intuitively though, it works for similar reasons as why regular induction works. P(0) or the base case works which causes P(1) or the leaf node to work which causes P(2) to work and so on. For this problem, it’s easy to combine the results of the left and right subtrees. Just add the two numbers and then another 1 for the root. Here’s the code:

def count(node):

  return count(node.left) + count(node.right) + 1 if node else 0

You certainly won’t get a question this easy but the process is the same for trickier problems. Here’s another problem:

Given the root to a binary tree, return the deepest node.

Base case for this question actually can’t be null, because it’s not a real result that can be combined (null is not a node). Here we should use the leaf node as the base case and return itself.

The recursive step for this problem is a little bit different because we can’t actually use the results of the left and right subtrees directly. So we need to ask, what other information do we need to solve this question? It turns out if we tagged with each subresult node their depths, we could get the final solution by picking the higher depth leaf and then incrementing it:

def deepest(node):

    if node and not node.left and not node.right:

        return (node, 1) # Leaf and its depth



    if not node.left: # Then the deepest node is on the right subtree

        return increment_depth(deepest(node.right))

    elif not node.right: # Then the deepest node is on the left subtree

        return increment_depth(deepest(node.left))



    return increment_depth(

            max(deepest(node.left), deepest(node.right),

                    key=lambda x: x[1])) # Pick higher depth tuple and then increment its depth



def increment_depth(node_depth_tuple):

    node, depth = node_depth_tuple

    return (node, depth + 1)

Best of luck!

Marc

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given an array of integers and a number k, where 1 <= k <= length of the array, compute the maximum values of each subarray of length k.

For example, given array = [10, 5, 2, 7, 8, 7] and k = 3, we should get: [10, 7, 8, 8], since:

• 10 = max(10, 5, 2)
• 7 = max(5, 2, 7)
• 8 = max(2, 7, 8)
• 8 = max(7, 8, 7)

Do this in O(n) time and O(k) space. You can modify the input array in-place and you do not need to store the results. You can simply print them out as you compute them.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

A builder is looking to build a row of N houses that can be of K different colors. He has a goal of minimizing cost while ensuring that no two neighboring houses are of the same color.

Given an N by K matrix where the n^th row and k^th column represents the cost to build the n^th house with k^th color, return the minimum cost which achieves this goal.

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The Reviews Are In!

Buy The Book On Amazon

The Daily Coding Problem Book is out, and in just a couple weeks we've climbed to the top of the Algorithms category on Amazon!

The book is packed with the best of the best problems from the newsletter, organized by topic, and carefully designed to optimize your interview prep. With explanations of each core concept and diagrams illustrating the most common data structures and algorithms that pop up in coding interviews, you'll be able to solve the toughest problems in exactly the way interviewers want to see.

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In our book, you’ll learn about:

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• Dynamic Programming
• Backtracking
• Bit Manipulation
• Pathfinding
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• Data Structure Design
• System Design

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I got the job

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given two singly linked lists that intersect at some point, find the intersecting node. The lists are non-cyclical.

For example, given A = 3 -> 7 -> 8 -> 10 and B = 99 -> 1 -> 8 -> 10, return the node with value 8.

In this example, assume nodes with the same value are the exact same node objects.

Do this in O(M + N) time (where M and N are the lengths of the lists) and constant space.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Snapchat.

Given an array of time intervals (start, end) for classroom lectures (possibly overlapping), find the minimum number of rooms required.

For example, given [(30, 75), (0, 50), (60, 150)], you should return 2.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Given a dictionary of words and a string made up of those words (no spaces), return the original sentence in a list. If there is more than one possible reconstruction, return any of them. If there is no possible reconstruction, then return null.

For example, given the set of words 'quick', 'brown', 'the', 'fox', and the string "thequickbrownfox", you should return ['the', 'quick', 'brown', 'fox'].

Given the set of words 'bed', 'bath', 'bedbath', 'and', 'beyond', and the string "bedbathandbeyond", return either ['bed', 'bath', 'and', 'beyond] or ['bedbath', 'and', 'beyond'].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

You are given an M by N matrix consisting of booleans that represents a board. Each True boolean represents a wall. Each False boolean represents a tile you can walk on.

Given this matrix, a start coordinate, and an end coordinate, return the minimum number of steps required to reach the end coordinate from the start. If there is no possible path, then return null. You can move up, left, down, and right. You cannot move through walls. You cannot wrap around the edges of the board.

For example, given the following board:

[[f, f, f, f],

[t, t, f, t],

[f, f, f, f],

[f, f, f, f]]

and start = (3, 0) (bottom left) and end = (0, 0) (top left), the minimum number of steps required to reach the end is 7, since we would need to go through (1, 2) because there is a wall everywhere else on the second row.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Implement locking in a binary tree. A binary tree node can be locked or unlocked only if all of its descendants or ancestors are not locked.

Design a binary tree node class with the following methods:

• is_locked, which returns whether the node is locked
• lock, which attempts to lock the node. If it cannot be locked, then it should return false. Otherwise, it should lock it and return true.
• unlock, which unlocks the node. If it cannot be unlocked, then it should return false. Otherwise, it should unlock it and return true.

You may augment the node to add parent pointers or any other property you would like. You may assume the class is used in a single-threaded program, so there is no need for actual locks or mutexes. Each method should run in O(h), where h is the height of the tree.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Implement regular expression matching with the following special characters:

• . (period) which matches any single character
• * (asterisk) which matches zero or more of the preceding element

That is, implement a function that takes in a string and a valid regular expression and returns whether or not the string matches the regular expression.

For example, given the regular expression "ra." and the string "ray", your function should return true. The same regular expression on the string "raymond" should return false.

Given the regular expression ".*at" and the string "chat", your function should return true. The same regular expression on the string "chats" should return false.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a singly linked list and an integer k, remove the k^th last element from the list. k is guaranteed to be smaller than the length of the list.

The list is very long, so making more than one pass is prohibitively expensive.

Do this in constant space and in one pass.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a string of round, curly, and square open and closing brackets, return whether the brackets are balanced (well-formed).

For example, given the string "([])[]({})", you should return true.

Given the string "([)]" or "((()", you should return false.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Palantir.

Write an algorithm to justify text. Given a sequence of words and an integer line length k, return a list of strings which represents each line, fully justified.

More specifically, you should have as many words as possible in each line. There should be at least one space between each word. Pad extra spaces when necessary so that each line has exactly length k. Spaces should be distributed as equally as possible, with the extra spaces, if any, distributed starting from the left.

If you can only fit one word on a line, then you should pad the right-hand side with spaces.

Each word is guaranteed not to be longer than k.

For example, given the list of words ["the", "quick", "brown", "fox", "jumps", "over", "the", "lazy", "dog"] and k = 16, you should return the following:

["the  quick brown", # 1 extra space on the left

"fox  jumps  over", # 2 extra spaces distributed evenly

"the   lazy   dog"] # 4 extra spaces distributed evenly

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Run-length encoding is a fast and simple method of encoding strings. The basic idea is to represent repeated successive characters as a single count and character. For example, the string "AAAABBBCCDAA" would be encoded as "4A3B2C1D2A".

Implement run-length encoding and decoding. You can assume the string to be encoded have no digits and consists solely of alphabetic characters. You can assume the string to be decoded is valid.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

You are given an array of non-negative integers that represents a two-dimensional elevation map where each element is unit-width wall and the integer is the height. Suppose it will rain and all spots between two walls get filled up.

Compute how many units of water remain trapped on the map in O(N) time and O(1) space.

For example, given the input [2, 1, 2], we can hold 1 unit of water in the middle.

Given the input [3, 0, 1, 3, 0, 5], we can hold 3 units in the first index, 2 in the second, and 3 in the fourth index (we cannot hold 5 since it would run off to the left), so we can trap 8 units of water.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

The edit distance between two strings refers to the minimum number of character insertions, deletions, and substitutions required to change one string to the other. For example, the edit distance between “kitten” and “sitting” is three: substitute the “k” for “s”, substitute the “e” for “i”, and append a “g”.

Given two strings, compute the edit distance between them.

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Hey there,

Today I'd like to give you some tips on how to solve backtracking questions. Backtracking is an effective technique for solving algorithmic problems. In backtracking, we search depth-first for solutions, backtracking to the last valid path as soon as we hit a dead end.

Backtracking reduces the search space since we no longer have to follow down any paths we know are invalid. This is called pruning. We must be able to test partial solutions: for example, we can't find a global optimum using backtracking, since we have no idea if the solution we're currently on can lead to it or not. But we can, for example, solve Sudoku using backtracking. We can know immediately if our solution so far is invalid by testing if two of the same number appear in the same row, column, or square.

Let's go through several examples of problems that can be nicely solved with backtracking to drill this concept down.

1. The N queens puzzle

The N queens puzzle is the classic backtracking problem. The question is this:

You have an N by N board. Write a function that returns the number of possible arrangements of the board where N queens can be placed on the board without threatening each other, i.e. no two queens share the same row, column, or diagonal.

Before continuing, you should take some time to try to solve it on your own!

First off, let's describe the brute force solution to this problem, which means trying every single combination of N queens in each of N * N spots. That's n² choose n, which is painfully slow. We can immediately improve the runtime of this algorithm by noticing that there's no point in ever placing two queens on the same row (or column), so we really only need to have one queen per row. Now, using brute force, we need to iterate over each row and over each spot on each row. Since we have N rows and N columns, our runtime will be O(N^N). That's still hella slow, though.

It's helpful to ask ourselves three questions to determine whether we can apply backtracking to a problem.

Can we construct a partial solution?

Yes, we can tentatively place queens on the board.

Can we verify if the partial solution is invalid?

Yes, we can check a solution is invalid if two queens threaten each other. To speed this up, we can assume that all queens already placed so far do not threaten each other, so we only need to check if the last queen we added attacks any other queen.

Can we verify if the solution is complete?

Yes, we know a solution is complete if all N queens have been placed.

Now that we are confident that we can use backtracking, let's apply it to this problem. We'll loop through the first row and try placing a queen in column 0..N, and then the second, and so on up until N. What differs here from brute force is that we'll be adding the queens incrementally instead of all at once.

We'll create an is_valid function that will check the board on each incremental addition. is_valid will look at the last queen placed and see if any other queen can threaten it. If so, then we prune the branch since there's no point pursuing it. Otherwise, we'll recursively call ourselves with the new incremental solution. We only stop once we hit the base case: we've placed all queens on the board already.

We can represent our board as just a 1D array of integers from 1..N, where the value at the index i that represents the column the queen on row i is on. Since we're working incrementally, we don't even need to have the whole board initialized. We can just append and pop as we go down the stack.

Here's the actual code in Python:

def n_queens(n, board=[]):

    if n == len(board):

        return 1



    count = 0

    for col in range(n):

        board.append(col)

        if is_valid(board):

            count += n_queens(n, board)

        board.pop()

    return count



def is_valid(board):

    current_queen_row, current_queen_col = len(board) - 1, board[-1]

    # Check if any queens can attack the last queen.

    for row, col in enumerate(board[:-1]):

        diff = abs(current_queen_col - col)

        if diff == 0 or diff == current_queen_row - row:

            return False

    return True

Let's try it out.

for i in range(10):

    print(n_queens(i))

1

1

0

0

2

10

4

40

92

352

Looks correct, according to OEIS!

2. Flight itinerary problem

The flight itinerary problem is as follows:

Given an unordered list of flights taken by someone, each represented as (origin, destination) pairs, and a starting airport, compute the person's itinerary. If no such itinerary exists, return null. All flights must be used in the itinerary.

For example, given the following list of flights:

• HNL ➔ AKL
• YUL ➔ ORD
• ORD ➔ SFO
• SFO ➔ HNL

and starting airport YUL, you should return YUL ➔ ORD ➔ SFO ➔ HNL ➔ AKL. (This also happens to be the actual itinerary for the trip I'm about to take.)

You should take some time to try to solve it on your own! Notice that a greedy solution won't work, since it's possible to have a cycle in the graph.

Let's again describe the brute force solution to this problem, which is to try every permutation of flights and verify that it's a valid itinerary. That would be O(n!). Now let's ask ourselves if we can improve this with backtracking.

Can we construct a partial solution?

Yes, we can build an (incomplete) itinerary and extend it by adding more flights to the end.

Can we verify if the partial solution is invalid?

Yes, we can check a solution is invalid if 1) there are no flights leaving from our last destination and 2) there are still flights remaining that can be taken. Since we must use all flights, this means we're at a dead end.

Can we verify if the solution is complete?

Yes, we can check if a solution is complete if our itinerary uses all the flights.

Let's use this to construct our solution:

def get_itinerary(flights, current_itinerary):

    # If we've used up all the flights, we're done

    if not flights:

        return current_itinerary

    last_stop = current_itinerary[-1]

    for i, (origin, destination) in enumerate(flights):

        # Make a copy of flights without the current one to mark it as used

        flights_minus_current = flights[:i] + flights[i + 1:]

        current_itinerary.append(destination)

        if origin == last_stop:

            return get_itinerary(flights_minus_current, current_itinerary)

        current_itinerary.pop()

    return None

3. Sudoku

Here's the problem: solve a well-posed sudoku puzzle.

Let's try using backtracking:

Can we construct a partial solution?

Yes, we can fill in some portions of the board.

Can we verify if the partial solution is invalid?

Yes, we can check that the board is valid so far if there are no rows, columns, or squares that contain the same digit.

Can we verify if the solution is complete?

Yes, the solution is complete when the board has been filled up.

Let's try to solve it using our template. We'll try filling each empty cell one by one, and backtrack once we hit an invalid state. That'll look something like this:

EMPTY = 0



def sudoku(board):

    if is_complete(board):

        return board



    r, c = find_first_empty(board)

    # set r, c to a val from 1 to 9

    for i in range(1, 10):

        board[r][c] = i

        if valid_so_far(board):

            result = sudoku(board)

            if is_complete(result):

                return result

        board[r][c] = EMPTY

    return board



def is_complete(board):

    return all(all(val is not EMPTY for val in row) for row in board)



def find_first_empty(board):

    for i, row in enumerate(board):

        for j, val in enumerate(row):

            if val == EMPTY:

                return i, j

    return False



def valid_so_far(board):

    if not rows_valid(board):

        return False

    if not cols_valid(board):

        return False

    if not blocks_valid(board):

        return False

    return True



def rows_valid(board):

    for row in board:

        if duplicates(row):

            return False

    return True



def cols_valid(board):

    for j in range(len(board[0])):

        if duplicates([board[i][j] for i in range(len(board))]):

            return False

    return True



def blocks_valid(board):

    for i in range(0, 9, 3):

        for j in range(0, 9, 3):

            block = []

            for k in range(3):

                for l in range(3):

                    block.append(board[i + k][j + l])

            if duplicates(block):

                return False

    return True



def duplicates(arr):

    c = {}

    for val in arr:

        if val in c and val is not EMPTY:

            return True

        c[val] = True

    return False

Best of luck!

Marc

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Good morning! Here's your coding interview problem for today.

This problem was asked by Jane Street.

Suppose you are given a table of currency exchange rates, represented as a 2D array. Determine whether there is a possible arbitrage: that is, whether there is some sequence of trades you can make, starting with some amount A of any currency, so that you can end up with some amount greater than A of that currency.

There are no transaction costs and you can trade fractional quantities.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Compute the running median of a sequence of numbers. That is, given a stream of numbers, print out the median of the list so far on each new element.

Recall that the median of an even-numbered list is the average of the two middle numbers.

For example, given the sequence [2, 1, 5, 7, 2, 0, 5], your algorithm should print out:

2

1.5

2

3.5

2

2

2

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Good morning! Here's your coding interview problem for today.

This problem was asked by Quora.

Given a string, find the palindrome that can be made by inserting the fewest number of characters as possible anywhere in the word. If there is more than one palindrome of minimum length that can be made, return the lexicographically earliest one (the first one alphabetically).

For example, given the string "race", you should return "ecarace", since we can add three letters to it (which is the smallest amount to make a palindrome). There are seven other palindromes that can be made from "race" by adding three letters, but "ecarace" comes first alphabetically.

As another example, given the string "google", you should return "elgoogle".

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given an array of strictly the characters 'R', 'G', and 'B', segregate the values of the array so that all the Rs come first, the Gs come second, and the Bs come last. You can only swap elements of the array.

Do this in linear time and in-place.

For example, given the array ['G', 'B', 'R', 'R', 'B', 'R', 'G'], it should become ['R', 'R', 'R', 'G', 'G', 'B', 'B'].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Dropbox.

Given the root to a binary search tree, find the second largest node in the tree.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

The power set of a set is the set of all its subsets. Write a function that, given a set, generates its power set.

For example, given the set {1, 2, 3}, it should return {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.

You may also use a list or array to represent a set.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

You have an N by N board. Write a function that, given N, returns the number of possible arrangements of the board where N queens can be placed on the board without threatening each other, i.e. no two queens share the same row, column, or diagonal.

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Hey there,

Hope your interview practicing is going well! Let's work through the problem of uniformly picking a random element from a gigantic stream. This is a common interview question at companies like Google and Facebook.

Naively, we could process the stream and store all the elements we encounter in a list, find its size, and pick a random element from [0, size - 1]. The problem with this approach is that it would take O(N) space for a large N.

Instead, let's attempt to solve using loop invariants. On the ith iteration of our loop to pick a random element, let's assume we already picked an element uniformly from [0, i - 1]. In order to maintain the loop invariant, we would need to pick the ith element as the new random element at 1 / (i + 1) chance. For the base case where i = 0, let's say the random element is the first one. Then we know it works because

• For i = 0, we would've picked uniformly from [0, 0].
• For i > 0, before the loop began, any element K in [0, i - 1] had 1 / i chance of being chosen as the random element. We want K to have 1 / (i + 1) chance of being chosen after the iteration. This is the case since the chance of having being chosen already but not getting swapped with the ith element is 1 / i * (1 - (1 / (i + 1))) which is 1 / i * i / (i + 1) or 1 / (i + 1)

Let's see how the code would look:

import random



def pick(big_stream):

    random_element = None



    for i, e in enumerate(big_stream):

        if i == 0:

            random_element = e

        if random.randint(1, i + 1) == 1:

            random_element = e

    return random_element

Since we are only storing a single variable, this only takes up constant space!

Turns out this algorithm is called Reservoir Sampling. If you liked this problem and solution, sign up for our mailing list below for problems like these! You can also read our other post on how to solve tricky interview questions like this one here.

Best of luck!

Marc

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Good morning! Here's your coding interview problem for today.

This problem was asked by Dropbox.

Conway's Game of Life takes place on an infinite two-dimensional board of square cells. Each cell is either dead or alive, and at each tick, the following rules apply:

• Any live cell with less than two live neighbours dies.
• Any live cell with two or three live neighbours remains living.
• Any live cell with more than three live neighbours dies.
• Any dead cell with exactly three live neighbours becomes a live cell.

A cell neighbours another cell if it is horizontally, vertically, or diagonally adjacent.

Implement Conway's Game of Life. It should be able to be initialized with a starting list of live cell coordinates and the number of steps it should run for. Once initialized, it should print out the board state at each step. Since it's an infinite board, print out only the relevant coordinates, i.e. from the top-leftmost live cell to bottom-rightmost live cell.

You can represent a live cell with an asterisk (*) and a dead cell with a dot (.).

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given an array of integers where every integer occurs three times except for one integer, which only occurs once, find and return the non-duplicated integer.

For example, given [6, 1, 3, 3, 3, 6, 6], return 1. Given [13, 19, 13, 13], return 19.

Do this in O(N) time and O(1) space.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given an unordered list of flights taken by someone, each represented as (origin, destination) pairs, and a starting airport, compute the person's itinerary. If no such itinerary exists, return null. If there are multiple possible itineraries, return the lexicographically smallest one. All flights must be used in the itinerary.

For example, given the list of flights [('SFO', 'HKO'), ('YYZ', 'SFO'), ('YUL', 'YYZ'), ('HKO', 'ORD')] and starting airport 'YUL', you should return the list ['YUL', 'YYZ', 'SFO', 'HKO', 'ORD'].

Given the list of flights [('SFO', 'COM'), ('COM', 'YYZ')] and starting airport 'COM', you should return null.

Given the list of flights [('A', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'A')] and starting airport 'A', you should return the list ['A', 'B', 'C', 'A', 'C'] even though ['A', 'C', 'A', 'B', 'C'] is also a valid itinerary. However, the first one is lexicographically smaller.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a list of integers S and a target number k, write a function that returns a subset of S that adds up to k. If such a subset cannot be made, then return null.

Integers can appear more than once in the list. You may assume all numbers in the list are positive.

For example, given S = [12, 1, 61, 5, 9, 2] and k = 24, return [12, 9, 2, 1] since it sums up to 24.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Implement a stack that has the following methods:

• push(val), which pushes an element onto the stack
• pop(), which pops off and returns the topmost element of the stack. If there are no elements in the stack, then it should throw an error or return null.
• max(), which returns the maximum value in the stack currently. If there are no elements in the stack, then it should throw an error or return null.

Each method should run in constant time.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

We can determine how "out of order" an array A is by counting the number of inversions it has. Two elements A[i] and A[j] form an inversion if A[i] > A[j] but i < j. That is, a smaller element appears after a larger element.

Given an array, count the number of inversions it has. Do this faster than O(N^2) time.

You may assume each element in the array is distinct.

For example, a sorted list has zero inversions. The array [2, 4, 1, 3, 5] has three inversions: (2, 1), (4, 1), and (4, 3). The array [5, 4, 3, 2, 1] has ten inversions: every distinct pair forms an inversion.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Two Sigma.

Using a function rand5() that returns an integer from 1 to 5 (inclusive) with uniform probability, implement a function rand7() that returns an integer from 1 to 7 (inclusive).

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given a string, find the longest palindromic contiguous substring. If there are more than one with the maximum length, return any one.

For example, the longest palindromic substring of "aabcdcb" is "bcdcb". The longest palindromic substring of "bananas" is "anana".

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a array of numbers representing the stock prices of a company in chronological order, write a function that calculates the maximum profit you could have made from buying and selling that stock once. You must buy before you can sell it.

For example, given [9, 11, 8, 5, 7, 10], you should return 5, since you could buy the stock at 5 dollars and sell it at 10 dollars.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given pre-order and in-order traversals of a binary tree, write a function to reconstruct the tree.

For example, given the following preorder traversal:

[a, b, d, e, c, f, g]

And the following inorder traversal:

[d, b, e, a, f, c, g]

You should return the following tree:

    a

   / \

  b   c

 / \ / \

d  e f  g

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given an array of numbers, find the maximum sum of any contiguous subarray of the array.

For example, given the array [34, -50, 42, 14, -5, 86], the maximum sum would be 137, since we would take elements 42, 14, -5, and 86.

Given the array [-5, -1, -8, -9], the maximum sum would be 0, since we would not take any elements.

Do this in O(N) time.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Suppose an arithmetic expression is given as a binary tree. Each leaf is an integer and each internal node is one of '+', '−', '∗', or '/'.

Given the root to such a tree, write a function to evaluate it.

For example, given the following tree:

    *

   / \

  +    +

 / \  / \

3  2  4  5

You should return 45, as it is (3 + 2) * (4 + 5).

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a function that generates perfectly random numbers between 1 and k (inclusive), where k is an input, write a function that shuffles a deck of cards represented as an array using only swaps.

It should run in O(N) time.

Hint: Make sure each one of the 52! permutations of the deck is equally likely.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Apple.

Implement a queue using two stacks. Recall that a queue is a FIFO (first-in, first-out) data structure with the following methods: enqueue, which inserts an element into the queue, and dequeue, which removes it.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Dropbox.

Sudoku is a puzzle where you're given a partially-filled 9 by 9 grid with digits. The objective is to fill the grid with the constraint that every row, column, and box (3 by 3 subgrid) must contain all of the digits from 1 to 9.

Implement an efficient sudoku solver.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Implement a URL shortener with the following methods:

• shorten(url), which shortens the url into a six-character alphanumeric string, such as zLg6wl.
• restore(short), which expands the shortened string into the original url. If no such shortened string exists, return null.

Hint: What if we enter the same URL twice?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given an undirected graph represented as an adjacency matrix and an integer k, write a function to determine whether each vertex in the graph can be colored such that no two adjacent vertices share the same color using at most k colors.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

An sorted array of integers was rotated an unknown number of times.

Given such an array, find the index of the element in the array in faster than linear time. If the element doesn't exist in the array, return null.

For example, given the array [13, 18, 25, 2, 8, 10] and the element 8, return 4 (the index of 8 in the array).

You can assume all the integers in the array are unique.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Implement a file syncing algorithm for two computers over a low-bandwidth network. What if we know the files in the two computers are mostly the same?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a multiset of integers, return whether it can be partitioned into two subsets whose sums are the same.

For example, given the multiset {15, 5, 20, 10, 35, 15, 10}, it would return true, since we can split it up into {15, 5, 10, 15, 10} and {20, 35}, which both add up to 55.

Given the multiset {15, 5, 20, 10, 35}, it would return false, since we can't split it up into two subsets that add up to the same sum.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Implement integer exponentiation. That is, implement the pow(x, y) function, where x and y are integers and returns x^y.

Do this faster than the naive method of repeated multiplication.

For example, pow(2, 10) should return 1024.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

There is an N by M matrix of zeroes. Given N and M, write a function to count the number of ways of starting at the top-left corner and getting to the bottom-right corner. You can only move right or down.

For example, given a 2 by 2 matrix, you should return 2, since there are two ways to get to the bottom-right:

• Right, then down
• Down, then right

Given a 5 by 5 matrix, there are 70 ways to get to the bottom-right.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Given a 2D matrix of characters and a target word, write a function that returns whether the word can be found in the matrix by going left-to-right, or up-to-down.

For example, given the following matrix:

[['F', 'A', 'C', 'I'],

 ['O', 'B', 'Q', 'P'],

 ['A', 'N', 'O', 'B'],

 ['M', 'A', 'S', 'S']]

and the target word 'FOAM', you should return true, since it's the leftmost column. Similarly, given the target word 'MASS', you should return true, since it's the last row.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

A knight's tour is a sequence of moves by a knight on a chessboard such that all squares are visited once.

Given N, write a function to return the number of knight's tours on an N by N chessboard.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given a N by M matrix of numbers, print out the matrix in a clockwise spiral.

For example, given the following matrix:

[[1,  2,  3,  4,  5],

 [6,  7,  8,  9,  10],

 [11, 12, 13, 14, 15],

 [16, 17, 18, 19, 20]]

You should print out the following:

1

2

3

4

5

10

15

20

19

18

17

16

11

6

7

8

9

14

13

12

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Good morning! Here's your coding interview problem for today.

This problem was asked by Square.

Assume you have access to a function toss_biased() which returns 0 or 1 with a probability that's not 50-50 (but also not 0-100 or 100-0). You do not know the bias of the coin.

Write a function to simulate an unbiased coin toss.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Implement an LFU (Least Frequently Used) cache. It should be able to be initialized with a cache size n, and contain the following methods:

• set(key, value): sets key to value. If there are already n items in the cache and we are adding a new item, then it should also remove the least frequently used item. If there is a tie, then the least recently used key should be removed.
• get(key): gets the value at key. If no such key exists, return null.

Each operation should run in O(1) time.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

On our special chessboard, two bishops attack each other if they share the same diagonal. This includes bishops that have another bishop located between them, i.e. bishops can attack through pieces.

You are given N bishops, represented as (row, column) tuples on a M by M chessboard. Write a function to count the number of pairs of bishops that attack each other. The ordering of the pair doesn't matter: (1, 2) is considered the same as (2, 1).

For example, given M = 5 and the list of bishops:

• (0, 0)
• (1, 2)
• (2, 2)
• (4, 0)

The board would look like this:

[b 0 0 0 0]

[0 0 b 0 0]

[0 0 b 0 0]

[0 0 0 0 0]

[b 0 0 0 0]

You should return 2, since bishops 1 and 3 attack each other, as well as bishops 3 and 4.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a list of integers, return the largest product that can be made by multiplying any three integers.

For example, if the list is [-10, -10, 5, 2], we should return 500, since that's -10 * -10 * 5.

You can assume the list has at least three integers.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

A number is considered perfect if its digits sum up to exactly 10.

Given a positive integer n, return the n-th perfect number.

For example, given 1, you should return 19. Given 2, you should return 28.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Two Sigma.

Using a function rand7() that returns an integer from 1 to 7 (inclusive) with uniform probability, implement a function rand5() that returns an integer from 1 to 5 (inclusive).

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

In a directed graph, each node is assigned an uppercase letter. We define a path's value as the number of most frequently-occurring letter along that path. For example, if a path in the graph goes through "ABACA", the value of the path is 3, since there are 3 occurrences of 'A' on the path.

Given a graph with n nodes and m directed edges, return the largest value path of the graph. If the largest value is infinite, then return null.

The graph is represented with a string and an edge list. The i-th character represents the uppercase letter of the i-th node. Each tuple in the edge list (i, j) means there is a directed edge from the i-th node to the j-th node. Self-edges are possible, as well as multi-edges.

For example, the following input graph:

ABACA

[(0, 1),

 (0, 2),

 (2, 3),

 (3, 4)]

Would have maximum value 3 using the path of vertices [0, 2, 3, 4], (A, A, C, A).

The following input graph:

A

[(0, 0)]

Should return null, since we have an infinite loop.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given the head of a singly linked list, reverse it in-place.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Apple.

Suppose you have a multiplication table that is N by N. That is, a 2D array where the value at the i-th row and j-th column is (i + 1) * (j + 1) (if 0-indexed) or i * j (if 1-indexed).

Given integers N and X, write a function that returns the number of times X appears as a value in an N by N multiplication table.

For example, given N = 6 and X = 12, you should return 4, since the multiplication table looks like this:

| 1 | 2 | 3 | 4 | 5 | 6 |

| 2 | 4 | 6 | 8 | 10 | 12 |

| 3 | 6 | 9 | 12 | 15 | 18 |

| 4 | 8 | 12 | 16 | 20 | 24 |

| 5 | 10 | 15 | 20 | 25 | 30 |

| 6 | 12 | 18 | 24 | 30 | 36 |

And there are 4 12's in the table.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Given an array of numbers, find the length of the longest increasing subsequence in the array. The subsequence does not necessarily have to be contiguous.

For example, given the array [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15], the longest increasing subsequence has length 6: it is 0, 2, 6, 9, 11, 15.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

You are given an N by M 2D matrix of lowercase letters. Determine the minimum number of columns that can be removed to ensure that each row is ordered from top to bottom lexicographically. That is, the letter at each column is lexicographically later as you go down each row. It does not matter whether each row itself is ordered lexicographically.

For example, given the following table:

cba

daf

ghi

This is not ordered because of the a in the center. We can remove the second column to make it ordered:

ca

df

gi

So your function should return 1, since we only needed to remove 1 column.

As another example, given the following table:

abcdef

Your function should return 0, since the rows are already ordered (there's only one row).

As another example, given the following table:

zyx

wvu

tsr

Your function should return 3, since we would need to remove all the columns to order it.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Snapchat.

Given a list of possibly overlapping intervals, return a new list of intervals where all overlapping intervals have been merged.

The input list is not necessarily ordered in any way.

For example, given [(1, 3), (5, 8), (4, 10), (20, 25)], you should return [(1, 3), (4, 10), (20, 25)].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given k sorted singly linked lists, write a function to merge all the lists into one sorted singly linked list.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given an array of integers, write a function to determine whether the array could become non-decreasing by modifying at most 1 element.

For example, given the array [10, 5, 7], you should return true, since we can modify the 10 into a 1 to make the array non-decreasing.

Given the array [10, 5, 1], you should return false, since we can't modify any one element to get a non-decreasing array.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given the root of a binary tree, return a deepest node. For example, in the following tree, return d.

    a

   / \

  b   c

 /

d

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Good morning! Here's your coding interview problem for today.

This problem was asked by Yelp.

Given a mapping of digits to letters (as in a phone number), and a digit string, return all possible letters the number could represent. You can assume each valid number in the mapping is a single digit.

For example if {“2”: [“a”, “b”, “c”], 3: [“d”, “e”, “f”], …} then “23” should return [“ad”, “ae”, “af”, “bd”, “be”, “bf”, “cd”, “ce”, “cf"].

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Good morning! Here's your coding interview problem for today.

This problem was asked Microsoft.

Using a read7() method that returns 7 characters from a file, implement readN(n) which reads n characters.

For example, given a file with the content “Hello world”, three read7() returns “Hello w”, “orld” and then “”.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Invert a binary tree.

For example, given the following tree:

    a

   / \

  b   c

 / \  /

d   e f

should become:

  a

 / \

 c  b

 \  / \

  f e  d

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given a matrix of 1s and 0s, return the number of "islands" in the matrix. A 1 represents land and 0 represents water, so an island is a group of 1s that are neighboring whose perimeter is surrounded by water.

For example, this matrix has 4 islands.

1 0 0 0 0

0 0 1 1 0

0 1 1 0 0

0 0 0 0 0

1 1 0 0 1

1 1 0 0 1

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given three 32-bit integers x, y, and b, return x if b is 1 and y if b is 0, using only mathematical or bit operations. You can assume b can only be 1 or 0.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a string of parentheses, write a function to compute the minimum number of parentheses to be removed to make the string valid (i.e. each open parenthesis is eventually closed).

For example, given the string "()())()", you should return 1. Given the string ")(", you should return 2, since we must remove all of them.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Uber.

A rule looks like this:

A NE B

This means this means point A is located northeast of point B.

A SW C

means that point A is southwest of C.

Given a list of rules, check if the sum of the rules validate. For example:

A N B

B NE C

C N A

does not validate, since A cannot be both north and south of C.

A NW B

A N B

is considered valid.

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Good morning! Here's your coding interview problem for today.

This question was asked by ContextLogic.

Implement division of two positive integers without using the division, multiplication, or modulus operators. Return the quotient as an integer, ignoring the remainder.

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Good morning! Here's your coding interview problem for today.

This problem was asked by LinkedIn.

Determine whether a tree is a valid binary search tree.

A binary search tree is a tree with two children, left and right, and satisfies the constraint that the key in the left child must be less than or equal to the root and the key in the right child must be greater than or equal to the root.

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Good morning! Here's your coding interview problem for today.

This question was asked by Google.

Given an integer n and a list of integers l, write a function that randomly generates a number from 0 to n-1 that isn't in l (uniform).

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Good morning! Here's your coding interview problem for today.

This problem was asked by Dropbox.

What does the below code snippet print out? How can we fix the anonymous functions to behave as we'd expect?

functions = []

for i in range(10):

    functions.append(lambda : i)



for f in functions:

    print(f())

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Good morning! Here's your coding interview problem for today.

This problem was asked by Airbnb.

We're given a hashmap associating each courseId key with a list of courseIds values, which represents that the prerequisites of courseId are courseIds. Return a sorted ordering of courses such that we can finish all courses.

Return null if there is no such ordering.

For example, given {'CSC300': ['CSC100', 'CSC200'], 'CSC200': ['CSC100'], 'CSC100': []}, should return ['CSC100', 'CSC200', 'CSCS300'].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Apple.

Given a tree, find the largest tree/subtree that is a BST.

Given a tree, return the size of the largest tree/subtree that is a BST.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a binary tree of integers, find the maximum path sum between two nodes. The path must go through at least one node, and does not need to go through the root.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Palantir.

Given a number represented by a list of digits, find the next greater permutation of a number, in terms of lexicographic ordering. If there is not greater permutation possible, return the permutation with the lowest value/ordering.

For example, the list [1,2,3] should return [1,3,2]. The list [1,3,2] should return [2,1,3]. The list [3,2,1] should return [1,2,3].

Can you perform the operation without allocating extra memory (disregarding the input memory)?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Given a number in the form of a list of digits, return all possible permutations.

For example, given [1,2,3], return [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Stripe.

Write a map implementation with a get function that lets you retrieve the value of a key at a particular time.

It should contain the following methods:

• set(key, value, time): sets key to value for t = time.
• get(key, time): gets the key at t = time.

The map should work like this. If we set a key at a particular time, it will maintain that value forever or until it gets set at a later time. In other words, when we get a key at a time, it should return the value that was set for that key set at the most recent time.

Consider the following examples:

d.set(1, 1, 0) # set key 1 to value 1 at time 0

d.set(1, 2, 2) # set key 1 to value 2 at time 2

d.get(1, 1) # get key 1 at time 1 should be 1

d.get(1, 3) # get key 1 at time 3 should be 2

d.set(1, 1, 5) # set key 1 to value 1 at time 5

d.get(1, 0) # get key 1 at time 0 should be null

d.get(1, 10) # get key 1 at time 10 should be 1

d.set(1, 1, 0) # set key 1 to value 1 at time 0

d.set(1, 2, 0) # set key 1 to value 2 at time 0

d.get(1, 0) # get key 1 at time 0 should be 2

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Good morning! Here's your coding interview problem for today.

This problem was asked by Coursera.

Given a 2D board of characters and a word, find if the word exists in the grid.

The word can be constructed from letters of sequentially adjacent cell, where "adjacent" cells are those horizontally or vertically neighboring. The same letter cell may not be used more than once.

For example, given the following board:

[

  ['A','B','C','E'],

  ['S','F','C','S'],

  ['A','D','E','E']

]

exists(board, "ABCCED") returns true, exists(board, "SEE") returns true, exists(board, "ABCB") returns false.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Given an unsorted array of integers, find the length of the longest consecutive elements sequence.

For example, given [100, 4, 200, 1, 3, 2], the longest consecutive element sequence is [1, 2, 3, 4]. Return its length: 4.

Your algorithm should run in O(n) complexity.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

You are in an infinite 2D grid where you can move in any of the 8 directions:

 (x,y) to

    (x+1, y),

    (x - 1, y),

    (x, y+1),

    (x, y-1),

    (x-1, y-1),

    (x+1,y+1),

    (x-1,y+1),

    (x+1,y-1)

You are given a sequence of points and the order in which you need to cover the points. Give the minimum number of steps in which you can achieve it. You start from the first point.

Example:

Input: [(0, 0), (1, 1), (1, 2)]

Output: 2

It takes 1 step to move from (0, 0) to (1, 1). It takes one more step to move from (1, 1) to (1, 2).

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Good morning! Here's your coding interview problem for today.

This problem was asked by Lyft.

Given a list of integers and a number K, return which contiguous elements of the list sum to K.

For example, if the list is [1, 2, 3, 4, 5] and K is 9, then it should return [2, 3, 4], since 2 + 3 + 4 = 9.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Determine whether a doubly linked list is a palindrome. What if it’s singly linked?

For example, 1 -> 4 -> 3 -> 4 -> 1 returns True while 1 -> 4 returns False.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Pinterest.

Given an integer list where each number represents the number of hops you can make, determine whether you can reach to the last index starting at index 0.

For example, [2, 0, 1, 0] returns True while [1, 1, 0, 1] returns False.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Print the nodes in a binary tree level-wise. For example, the following should print 1, 2, 3, 4, 5.

  1

 / \

2   3

   / \

  4   5

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given two strings A and B, return whether or not A can be shifted some number of times to get B.

For example, if A is abcde and B is cdeab, return true. If A is abc and B is acb, return false.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a binary tree, return all paths from the root to leaves.

For example, given the tree:

   1

  / \

 2   3

    / \

   4   5

Return [[1, 2], [1, 3, 4], [1, 3, 5]].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a word W and a string S, find all starting indices in S which are anagrams of W.

For example, given that W is "ab", and S is "abxaba", return 0, 3, and 4.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Twitter.

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree. Assume that each node in the tree also has a pointer to its parent.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a string of words delimited by spaces, reverse the words in string. For example, given "hello world here", return "here world hello"

Follow-up: given a mutable string representation, can you perform this operation in-place?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a string and a set of delimiters, reverse the words in the string while maintaining the relative order of the delimiters. For example, given "hello/world:here", return "here/world:hello"

Follow-up: Does your solution work for the following cases: "hello/world:here/", "hello//world:here"

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given two non-empty binary trees s and t, check whether tree t has exactly the same structure and node values with a subtree of s. A subtree of s is a tree consists of a node in s and all of this node's descendants. The tree s could also be considered as a subtree of itself.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Jane Street.

Generate a finite, but an arbitrarily large binary tree quickly in O(1).

That is, generate() should return a tree whose size is unbounded but finite.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a binary tree, return the level of the tree with minimum sum.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a sorted list of integers, square the elements and give the output in sorted order.

For example, given [-9, -2, 0, 2, 3], return [0, 4, 4, 9, 81].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given a set of closed intervals, find the smallest set of numbers that covers all the intervals. If there are multiple smallest sets, return any of them.

For example, given the intervals [0, 3], [2, 6], [3, 4], [6, 9], one set of numbers that covers all these intervals is {3, 6}.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Implement the singleton pattern with a twist. First, instead of storing one instance, store two instances. And in every even call of getInstance(), return the first instance and in every odd call of getInstance(), return the second instance.

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Good morning! Here's your coding interview problem for today.

This question was asked by Zillow.

You are given a 2-d matrix where each cell represents number of coins in that cell. Assuming we start at matrix[0][0], and can only move right or down, find the maximum number of coins you can collect by the bottom right corner.

For example, in this matrix

0 3 1 1

2 0 0 4

1 5 3 1

The most we can collect is 0 + 2 + 1 + 5 + 3 + 1 = 12 coins.

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Good morning! Here's your coding interview problem for today.

This problem was asked by LinkedIn.

Given a string, return whether it represents a number. Here are the different kinds of numbers:

• "10", a positive integer
• "-10", a negative integer
• "10.1", a positive real number
• "-10.1", a negative real number
• "1e5", a number in scientific notation

And here are examples of non-numbers:

• "a"
• "x 1"
• "a -2"
• "-"

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

You have n fair coins and you flip them all at the same time. Any that come up tails you set aside. The ones that come up heads you flip again. How many rounds do you expect to play before only one coin remains?

Write a function that, given n, returns the number of rounds you'd expect to play until one coin remains.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Write a function that rotates a list by k elements. For example, [1, 2, 3, 4, 5, 6] rotated by two becomes [3, 4, 5, 6, 1, 2]. Try solving this without creating a copy of the list. How many swap or move operations do you need?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Let's represent an integer in a linked list format by having each node represent a digit in the number. The nodes make up the number in reversed order.

For example, the following linked list:

1 -> 2 -> 3 -> 4 -> 5

is the number 54321.

Given two linked lists in this format, return their sum in the same linked list format.

For example, given

9 -> 9

5 -> 2

return 124 (99 + 25) as:

4 -> 2 -> 1

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Good morning! Here's your coding interview problem for today.

The Tower of Hanoi is a puzzle game with three rods and n disks, each a different size.

All the disks start off on the first rod in a stack. They are ordered by size, with the largest disk on the bottom and the smallest one at the top.

The goal of this puzzle is to move all the disks from the first rod to the last rod while following these rules:

• You can only move one disk at a time.
• A move consists of taking the uppermost disk from one of the stacks and placing it on top of another stack.
• You cannot place a larger disk on top of a smaller disk.

Write a function that prints out all the steps necessary to complete the Tower of Hanoi. You should assume that the rods are numbered, with the first rod being 1, the second (auxiliary) rod being 2, and the last (goal) rod being 3.

For example, with n = 3, we can do this in 7 moves:

Move 1 to 3

Move 1 to 2

Move 3 to 2

Move 1 to 3

Move 2 to 1

Move 2 to 3

Move 1 to 3

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Good morning! Here's your coding interview problem for today.

Given a real number n, find the square root of n. For example, given n = 9, return 3.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given an array of numbers representing the stock prices of a company in chronological order and an integer k, return the maximum profit you can make from k buys and sells. You must buy the stock before you can sell it, and you must sell the stock before you can buy it again.

For example, given k = 2 and the array [5, 2, 4, 0, 1], you should return 3.

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Good morning! Here's your coding interview problem for today.

This question was asked by Snapchat.

Given the head to a singly linked list, where each node also has a “random” pointer that points to anywhere in the linked list, deep clone the list.

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Good morning! Here's your coding interview problem for today.

This question was asked by Riot Games.

Design and implement a HitCounter class that keeps track of requests (or hits). It should support the following operations:

• record(timestamp): records a hit that happened at timestamp
• total(): returns the total number of hits recorded
• range(lower, upper): returns the number of hits that occurred between timestamps lower and upper (inclusive)

Follow-up: What if our system has limited memory?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given a node in a binary search tree, return the next bigger element, also known as the inorder successor.

For example, the inorder successor of 22 is 30.

   10

  /  \

 5    30

     /  \

   22    35

You can assume each node has a parent pointer.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

You have a large array with most of the elements as zero.

Use a more space-efficient data structure, SparseArray, that implements the same interface:

• init(arr, size): initialize with the original large array and size.
• set(i, val): updates index at i with val.
• get(i): gets the value at index i.

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Good morning! Here's your coding interview problem for today.

This question was asked by Apple.

Given a binary tree, find a minimum path sum from root to a leaf.

For example, the minimum path in this tree is [10, 5, 1, -1], which has sum 15.

  10

 /  \

5    5

 \     \

   2    1

       /

     -1

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Good morning! Here's your coding interview problem for today.

This question was asked by Google.

Given an N by M matrix consisting only of 1's and 0's, find the largest rectangle containing only 1's and return its area.

For example, given the following matrix:

[[1, 0, 0, 0],

 [1, 0, 1, 1],

 [1, 0, 1, 1],

 [0, 1, 0, 0]]

Return 4.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Implement a bit array.

A bit array is a space efficient array that holds a value of 1 or 0 at each index.

• init(size): initialize the array with size
• set(i, val): updates index at i with val where val is either 1 or 0.
• get(i): gets the value at index i.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Find the minimum number of coins required to make n cents.

You can use standard American denominations, that is, 1¢, 5¢, 10¢, and 25¢.

For example, given n = 16, return 3 since we can make it with a 10¢, a 5¢, and a 1¢.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given an iterator with methods next() and hasNext(), create a wrapper iterator, PeekableInterface, which also implements peek(). peek shows the next element that would be returned on next().

Here is the interface:

class PeekableInterface(object):

    def __init__(self, iterator):

        pass



    def peek(self):

        pass



    def next(self):

        pass



    def hasNext(self):

        pass

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given an array of integers in which two elements appear exactly once and all other elements appear exactly twice, find the two elements that appear only once.

For example, given the array [2, 4, 6, 8, 10, 2, 6, 10], return 4 and 8. The order does not matter.

Follow-up: Can you do this in linear time and constant space?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Microsoft.

Implement 3 stacks using a single list:

class Stack:

    def __init__(self):

        self.list = []



    def pop(self, stack_number):

        pass



    def push(self, item, stack_number):

        pass

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

You're given a string consisting solely of (, ), and *. * can represent either a (, ), or an empty string. Determine whether the parentheses are balanced.

For example, (()* and (*) are balanced. )*( is not balanced.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given a pivot x, and a list lst, partition the list into three parts.

• The first part contains all elements in lst that are less than x
• The second part contains all elements in lst that are equal to x
• The third part contains all elements in lst that are larger than x

Ordering within a part can be arbitrary.

For example, given x = 10 and lst = [9, 12, 3, 5, 14, 10, 10], one partition may be [9, 3, 5, 10, 10, 12, 14].

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Good morning! Here's your coding interview problem for today.

This problem was asked by Google.

Given an array of numbers and an index i, return the index of the nearest larger number of the number at index i, where distance is measured in array indices.

For example, given [4, 1, 3, 5, 6] and index 0, you should return 3.

If two distances to larger numbers are the equal, then return any one of them. If the array at i doesn't have a nearest larger integer, then return null.

Follow-up: If you can preprocess the array, can you do this in constant time?

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Good morning! Here's your coding interview problem for today.

This problem was asked by Goldman Sachs.

Given a list of numbers L, implement a method sum(i, j) which returns the sum from the sublist L[i:j] (including i, excluding j).

For example, given L = [1, 2, 3, 4, 5], sum(1, 3) should return sum([2, 3]), which is 5.

You can assume that you can do some pre-processing. sum() should be optimized over the pre-processing step.

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Good morning! Here's your coding interview problem for today.

This problem was asked by LinkedIn.

Given a list of points, a central point, and an integer k, find the nearest k points from the central point.

For example, given the list of points [(0, 0), (5, 4), (3, 1)], the central point (1, 2), and k = 2, return [(0, 0), (3, 1)].

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Good morning! Here's your coding interview problem for today.

Given a 2-D matrix representing an image, a location of a pixel in the screen and a color C, replace the color of the given pixel and all adjacent same colored pixels with C.

For example, given the following matrix, and location pixel of (2, 2), and 'G' for green:

B B W

W W W

W W W

B B B

Becomes

B B G

G G G

G G G

B B B

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Good morning! Here's your coding interview problem for today.

This problem was asked by Triplebyte.

You are given n numbers as well as n probabilities that sum up to 1. Write a function to generate one of the numbers with its corresponding probability.

For example, given the numbers [1, 2, 3, 4] and probabilities [0.1, 0.5, 0.2, 0.2], your function should return 1 10% of the time, 2 50% of the time, and 3 and 4 20% of the time.

You can generate random numbers between 0 and 1 uniformly.

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Good morning! Here's your coding interview problem for today.

Find an efficient algorithm to find the smallest distance (measured in number of words) between any two given words in a string.

For example, given words "hello", and "world" and a text content of "dog cat hello cat dog dog hello cat world", return 1 because there's only one word "cat" in between the two words.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Implement a stack API using only a heap. A stack implements the following methods:

• push(item), which adds an element to the stack
• pop(), which removes and returns the most recently added element (or throws an error if there is nothing on the stack)

Recall that a heap has the following operations:

• push(item), which adds a new key to the heap
• pop(), which removes and returns the max value of the heap

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Good morning! Here's your coding interview problem for today.

This problem was asked by MongoDB.

Given a list of elements, find the majority element, which appears more than half the time (> floor(len(lst) / 2.0)).

You can assume that such element exists.

For example, given [1, 2, 1, 1, 3, 4, 0], return 1.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Amazon.

Given a string, determine whether any permutation of it is a palindrome.

For example, carrace should return true, since it can be rearranged to form racecar, which is a palindrome. daily should return false, since there's no rearrangement that can form a palindrome.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Slack.

You are given an N by M matrix of 0s and 1s. Starting from the top left corner, how many ways are there to reach the bottom right corner?

You can only move right and down. 0 represents an empty space while 1 represents a wall you cannot walk through.

For example, given the following matrix:

[[0, 0, 1],

 [0, 0, 1],

 [1, 0, 0]]

Return two, as there are only two ways to get to the bottom right:

• Right, down, down, right
• Down, right, down, right

The top left corner and bottom right corner will always be 0.

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Good morning! Here's your coding interview problem for today.

This problem was asked by Facebook.

Given a positive integer n, find the smallest number of squared integers which sum to n.

For example, given n = 13, return 2 since 13 = 3² + 2² = 9 + 4.

Given n = 27, return 3 since 27 = 3² + 3² + 3² = 9 + 9 + 9.

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